Related papers: Randomness is valid at large numbers
In the classical probability in continuous random variables there is no distinguishing between the probability involving strict inequality and non strict inequality. Moreover a probability involves equality collapse to zero without…
The procedure of tossing quantum coins and dice is described. This case is an important example of a quantum procedure because it presents a typical framework employed in quantum information processing and quantum computing. The emphasis is…
Randomness is a valuable resource in science, cryptography, engineering, and information technology. Quantum-mechanical sources of randomness are attractive because of the indeterminism of individual quantum processes. Here we consider the…
Probability interference is a fundamental characteristic of quantum mechanics. In this paper we attempt to show with the help of some examples, where this fundamental trait of quantum physics can be found back in a social science…
The authors of a recent paper [Phys. Rev. Lett. 113, 120404 (2014)] suggest that "weak values are not inherently quantum but rather a purely statistical feature of pre- and postselection with disturbance". We argue that this claim is…
An infinite binary sequence is deemed to be random if it has all definable properties that hold almost surely for the usual probability measure on the set of infinite binary sequences. There are only countably many such properties, so it…
This note proves a law of large numbers for predicting several steps ahead, which, in the case of uniformly bounded random variables, generalizes the standard law of large numbers for martingales; the standard law of large numbers…
A distinction is sometimes made between "statistical" and "subjective" probabilities. This is based on a distinction between "unique" events and "repeatable" events. We argue that this distinction is untenable, since all events are "unique"…
In classical probability theory, the convergence of empirical frequencies to theoretical probabilities: as captured by the Law of Large Numbers (LLN): is treated as axiomatic and emergent from statistical assumptions such as independence…
We report a rigorous theory to show the origin of the unexpected periodic behavior seen in the consecutive differences between prime numbers. We also check numerically our findings to ensure that they hold for finite sequences of primes,…
The Law of Large Numbers tells us that as the sample size (N) is increased, the sample mean converges on the population mean, provided that the latter exists. In this paper, we investigate the opposite effect: keeping the sample size fixed…
For a stochastic process reset at random times, we discuss to what extent the probabilities of some orderings of observables associated with the intervals of time between resetting events are universal, i.e., independent of the choice of…
Complex numbers play a crucial role in quantum mechanics. However, their necessity remains debated: whether they are fundamental or merely convenient. Recently, it was claimed that quantum mechanics based on real numbers can be…
A statistical analysis of the prime numbers indicates possible traces of quantum chaos. We have computed the nearest neighbor spacing distribution, number variance, skewness, and excess for sequences of the first N primes for various values…
We establish a strong law of large numbers for one-dimensional continuous-time random walks in dynamic random environments under two main assumptions: the environment is required to satisfy a decoupling inequality that can be interpreted as…
Take a look around you -- in your family, your school or workplace, in the streets, and you see boys & girls in about equal proportion, and without any easily visible gender patterns in case of siblings. So, to the famous first order of…
This paper questions the generally accepted assumption that one can make a random choice that is independent of the rest of the universe. We give a general description of any setup that could be conceived to generate random numbers. Based…
We prove an analogue of the classical ballot theorem that holds for any random walk in the range of attraction of the normal distribution. Our result is best possible: we exhibit examples demonstrating that if any of our hypotheses are…
To test the limits of quantum mechanics, a proposal for an experiment on protons is suggested. The spin component of proton is measured very rapidly in sequential measurements. The reason for this experiment is derived from the genuine…
Given entropy's central role in multiple areas of physics and science, one important task is to develop a systematic and unifying approach to defining entropy. Games of chance become a natural candidate for characterising the uncertainty of…